We are asked to choose the reason why [tex]\frac{3}{5}[/tex] is the exact quotient for [tex]\frac{1}{2}[/tex] divided by [tex]\frac{5}{6}[/tex].
We know that divisor is the number that we divide with. The quotient is the answer to any division problem. Dividend is the number that we want to divide.
[tex]\text{Dividend}=\text{Quotient}\times \text{Divisor}[/tex]
We can see that is our given problem dividend is [tex]\frac{1}{2}[/tex], quotient is [tex]\frac{3}{5}[/tex] and divisor is [tex]\frac{5}{6}[/tex]. Upon multiplying quotient with divisor, we will get:
[tex]\text{Dividend}=\frac{3}{5}\times \frac{5}{6}[/tex]
We can cancel out 5 from numerator and denominator.
[tex]\frac{1}{2}=\frac{3}{1}\times \frac{1}{6}[/tex]
[tex]\frac{1}{2}=\frac{3}{6}[/tex]
[tex]\frac{1}{2}=\frac{3\times 1}{3\times 2}[/tex]
[tex]\frac{1}{2}=\frac{1}{2}[/tex]
Since both sides are equal, therefore, last option [tex]\frac{3}{5}\times \frac{5}{6}=\frac{1}{2}[/tex] is the correct choice.
